We show that if a homogeneous polynomial f in n variables has Waring rank \(n+1\), then the corresponding projective hypersurface \(f=0\) has at most isolated singularities, and the type of these singularities is completely determined by the combinatorics of a hyperplane arrangement naturally associated with the Waring decomposition of f. We also discuss the relation between the Waring rank and the type of singularities on a plane curve, when this curve is defined by the suspension of a binary form, or when the Waring rank is 5.

中文翻译：

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对称张量的警告等级和某些投影超曲面的奇异性

我们表明，如果一个均匀的多项式˚F在Ñ变量具有韦林氏秩\（N + 1 \） ，则相应的投影超曲面\（F = 0 \）具有至多分离奇点，这些奇点的类型完全被确定自然与f的Waring分解有关的超平面布置的组合。当该曲线由二进制形式的悬浮定义或当Waring等级为5时，我们还将讨论Waring等级与奇异类型之间的关系。